I can't tell if that's a cut or a brush burn. Either way i don't think hair is ever going to grow there again. there might not be a visible scar on the skin when it heals, but i doubt your gonna see any hair grow back.

Horse Trick:
Paliminos are light horses, and if they get a bad scrape the hair often grows back in dark (if it grows in at all). A friend of mine has a halter show stallion and he ripped himself open on a fence. She used cold bacon grease on the scab twice a day, the hair grew back quickly and was not darkened. It doesn't hurt to try... of course, there is the difficulty in getting the dog not to lick it incessently...